UNIVERSITY    OF    CALIFORNIA  agricultural  Experiment  Station 

COLLEGE    OF   AGRICULTURE  E-   J-   WlCKSON,    Director 

BERKELEY,    CALIFORNIA 


CIRCULAR  No.  50 

(April,  1910) 


FUMIGATION    SCHEDULING 


BY 

0.  W..  WOODWORTH. 


The  art  of  fumigation  has  gone  so  far  in  advance  of  the  science 
of  fumigation  that  many  fumigators  have  at  times  felt  that  science 
had  nothing  of  value  to  offer  the  practical  fumigator.  As  in  every 
other  practical  art,  a  point  is  finally  reached — in  this  case  has  long 
been  reached— where  further  progress  is  impossible  without  resorting 
to  more  accurate  methods. 

Foremost  of  all  the  problems  of  fumigation  is  the  securing  of 
accuracy  in  scheduling  an  orchard,  because  both  efficiency  and  econ- 
omy depend  more  on  this  factor  than  upon  any  other. 

While  there  may  be  reason  for  difference  of  opinion  as  to  the 
amount  it  is  proper  to  use  at  different  times  of  the  year,  for  different 
insects,  or  for  trees  of  different  size,  there  is  no  difference  of  opinion 
possible  in  regard  to  the  contention  that  trees  alike  in  all  respects 
should  have  equal  dose.  We  have  records  of  the  work  of  about  forty 
fumigators  and  not  one  was  found  who  did  not  vary  in  his  judgment 
in  trees  of  identical  size  to  the  extent  of  at  least  fifty  per  cent. 

Fumigators  very  generally  recognize  the  desirability  of  measuring 
instead  of  guessing  the  size  of  trees  and  would  no  doubt  have  long 
ago  adopted  the  practice  had  there  been  an  acceptable  method  avail- 
able, and  orchardists,  had  they  fully  realized  the  waste  resulting  from 
the  present  practice  and  the  possibility  of  more  uniform  killing  of 
the  scale  that  it  is  possible  to  secure,  would  have  insisted  upon  having 
the  trees  measured  with  as  much  care  as  is  given  to  weighing  the 
cyanide. 

This  Experiment  Station  urged  the  measurement  of  tents  from 
the  first  and  developed  all  the  practical  methods  of  measurement  thus 
far  proposed.  In  the  first  work  on  fumigation,  Bulletin  No.  71, 
printed  in  1887,  Mr.  Morse  used  direct  measurement  of  height  and 


Fig.  1. — One  method  of  marking  fumigation  tents  to  indicate  dosage. 


Fig.  2. — The  method  of  measuring  tents  employed  in  securing  some  of  the 
data  discussed  in  this  Bulletin. 


3 

diameter.  This  was  done  by  the  use  of  poles  or  tapes.  His  table  only 
gives  dosage  for  tents  in  which  these  dimensions  are  equal.  Subse- 
quent writers  adopted  the  same  plan,  but  gave  the  dosage  for  trees  in 
which  the  two  dimensions  differed. 

The  first  suggested  change  in  the  method  of  obtaining  dimensions 
was  in  1894,  in  Bulletin  No.  122,  where  the  idea  of  first  covering  the 
tree  with  a  tent  and  then  measuring  the  distance  over  the  top  and 
that  around  near  the  bottom  was  suggested  and  an  elaborate  table  was 
presented  for  obtaining  the  dosage  from  these  measurements.  This 
method  was  practically  used  by  the  writer  in  the  field  in  1902  in 
fumigating  for  the  white  fly  in  the  Mantee  River  section  in  Florida, 
where  the  distance  over  the  tent  was  read  from  marks  placed  on  the 
tent  giving  the  distance  down  from  the  middle  of  the  top  in  feet.  A 
modification  of  this  plan  was  illustrated  in  1904,  in  Bulletin  No.  152 
(fig.  1),  where  the  actual  dosage  was  marked  on  the  tent  to  avoid  the 
inconvenience  of  calculation.  In  this  same  bulletin  a  rapid  method 
of  taking  the  measurement  with  lines  was  also  presented  (fig.  2)  and 
a  diagram  furnished  whereby  the  volume  could  be  read  at  once  from 
such  measurements  without  calculation.  No  special  effort  was  made 
by  the  Station  to  secure  the  adoption  of  any  of  these  methods,  and 
it  was  not  until  the  work  was  taken  up  by  the  United  States  Depart- 
ment of  Agriculture  that  finally  a  portion  of  the  practical  fumigators 
began  to  apply  the  method  of  measurement  by  marked  tents. 

The  interest  having  thus  been  aroused  it  will  be  opportune  to 
discuss  more  fully  than  has  as  yet  been  done,  the  available  methods 
of  measurement  and  calculation  and  to  describe  certain  recent  im- 
provements in  the  processes. 

THE  MEASUEEMENTS. 

If  the  tent  or  tree  is  calculated  as  a  regular  figure  the  area  or 
volume  may  be  calculated  from  (1)  the  height  and  diameter,  (2)  the 
circumference  and  height,  (3)  the  distance  over  and  height,  (4)  the 
distance  over  and  the  diameter,  or  (5)  the  "circumference  and  the 
distance  over,"  that  is,  from  any  combination  of  these  four  dimen- 
sions except  circumference  and  diameter,  since  the  former  is  only 
3.1416  times  the  latter  and  gives  no  clue  to  the  other  dimensions. 
The  distance  over,  however,  consists  of  half  the  circumference  plus 
twice  the  height  minus  the  diameter  and  will  therefore  give  either 
height  or  diameter  if  the  other  is  known.  All  of  these  dimensions 
may  be  determined  optically  from  the  ground  except  the  circumfer- 
ence, and  all  of  them  can  be  measured  directly. 


Direct  measurements. — These  may  be  made  in  three  ways:  by 
pacing,  by  the  use  of  a  pole,  or  by  a  tape.  Pacing  is  the  least  accur- 
ate, but  decidedly  better  than  the  practice  of  guessing.  It  is  available 
only  for  diameter  and  circumference  and  therefore  must  be  supple- 
mented by  another  measurement  to  give  the  height.  Since  the  cir- 
cumference is  over  three  times  as  long  as  the  diameter  it  is  to  a  corre- 
sponding degree  more  accurate.  The  use  of  a  pole  is  the  most  prac- 
tical accurate  method  of  direct  measurement  for  either  height  or 
diameter.  To  obtain  the  diameter  the  pole  is  thrust  through  the  tree 
from  one  side  until  it  hits  the  trunk,  giving  a  semidiameter,  or  until 
the  end  just  corresponds  with  the  edge  of  the  foliage  when  by  walking 
around  the  tree  the  amount  projecting  will  enable  us  to  determine  the 
diameter.  To  obtain  the  height  the  pole  must  be  stood  upright  next 
to  the  trunk.  The  best  way  is  to  use  two  short  poles,  only  one  of 
which  need  be  graduated,  and  either  may  be  elevated  until  it  reaches 
the  top  of  the  tree. 

The  tape  is  not  practical  except  after  the  tent  is  on  the  tree,  and 
onry  for  circumference  and  distance  over.  To  obtain  the  circum- 
ference requires  a  trip  around  the  tree.  The  distance  over  is  prob- 
ably best  secured  by  graduating  the  tent,  making  it  in  effect  a  tape. 
If  a  loose  tape  is  used  one  end  may  be  thrown  over  the  tent  or  the 
tape  may  be  put  in  position  by  the  use  of  a  light  fishpole,  as  described 
in  Bulletin  No.  152  (fig.  2).  In  this  case  the  distance  over  is  first 
taken  by  going  half  way  around  the  tent  and  the  line  then  lowered 
by  the  use  of  the  pole  and  the  circumference  determined  after  going 
the  remainder  of  the  way  round.  This  and  the  use  of  marked  tents 
are  undoubtedly  the  most  rapid  of  all  direct  measurements,  and  the 
latter  the  most  practical  method  for  field  work  where  extreme  accuracy 
is  required.  As  will  be  explained  below,  judgment  must  be  used  in 
measuring  trees  or  the  results  may  be  very  far  from  accurate. 

Optical  methods. — The  different  size  of  trees  is  so  evident  to  the 
eye  that  it  is  not  strange  that  fumigators  have  been  convinced  that 
their  judgment  was  sufficiently  accurate  to  replace  the  slow  and  diffi- 
cult methods  heretofore  available  for  measuring  trees.  All  optical 
methods  of  measurement,  like  surveying,  are  based  upon  the  com- 
parison of  similar  triangles  (ABC  and  ADE,  fig.  3),  and  depend 
upon  the  fact  that  the  sides  of  similar  triangles  are  exactly  propor- 
tional to  each  other,  thus  in  figure  3,  if  the  line  AB,  BC,  and  AD  are 
all  known  one  can  calculate  the  length  of  DE.  Four  methods  have 
occurred  to  us  as  available  for  optical  measurement  and  more  or  less 
completely  tested  out.     These  consist  in  applying  the  principle  of  the 


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(1)  photo  camera,   (2)   the  magic  lantern,   (3)   displacement  mirrors, 
and  (4)  direct  vision. 


Fig.  3. — Optical  measurement  depends  on  the  fact  that 


AB 
BC 


AD 

DE' 


The  photo  camera  method  was  first  proposed  by  Mr.  W.  B.  Parker, 
a  student  and  assistant  in  the  Department,  and  largely  worked  out 
and  tested  by  him.  The  idea  was  to  examine  the  tree  on  the  ground 
glass  from  a  definite  distance,  either  determined  by  the  position  of 
adjacent  trees  or  by  the  sharpness  of  the  image,  and  to  dose  the  tree 
according  to  a  diagram  drawn  on  the  ground  glass.  Referring  again 
to  figure  3.  the  lines  AB  and  AD  are  thus  invariable  and  the  size  of 
the  tent  determined  by  the  length  of  BC  in  the  two  dimensions.  It 
would  be  possible  to  maintain  AB  and  BC  as  invariable  for  diameter 
and  measure  AD  as  described  below  under  direct  vision ;  indeed,  the 
camera  did  not  seem  to  present  any  advantage  over  the  other  method, 
and  was  therefore  discarded. 

The  Magic  lantern  method  is  particularly  available  for  night  work, 
but  has  not  yet  been  sufficiently  tested.  It  will  at  best  be  a  rela- 
tively expensive  instrument.  The  principle  is  to  approach  the  tree 
until  the  diameter  of  the  illumined  field  corresponds  with  the  width 
of  the  tree,  thus  maintaining  the  length  of  the  line  BC  constant  for 
the  diameter  and  arrange  an  oblique  slide  in  such  a  position  that  the 
appropriate  graduation  appears  in  focus  on  the  tent.  The  ratio  be- 
tween the  conjugate  foci  of  the  lenses  is  that  between  AB  and  AD  — 
AB  —  ^DE.  This  would  appear  to  be  the  most  rapid  and  least  liable 
to  error  of  all  night  methods,  since  after  the  instrument  is  once  ad- 
justed the  fumigator  need  only  see  that  he  is  in  such  a  position  that 
the  width  of  the  tent  is  in  the  light  when  bringing  the  top  of  the  field 
to  correspond  with  the  top  of  the  tent  the  figure  appearing  clearly  in 
focus  on  the  tent  nearest  the  ground  gives  the  proper  dose  in  ounces. 
Since  a  fumigator  carries  a  lantern  anyway  the  method  requires  no 
extra  apparatus. 

Displacement  mirrors  are  used  on  instruments  requiring  great 
precision,  such  as  sextants  and  may  prove  the  most  accurate  of  the 


optical  methods.  The  apparatus  will  be  somewhat  expensive,  but  will 
be  tested  out  more  fully  in  the  near  future. 

The  direct  vision  methods,  because  of  the  cheapness  and  simplicity 
of  the  apparatus  required,  will  without  doubt  be  more  acceptable  to 
fumigators  than  either  of  the  methods  mentioned  above.  They  are 
available  for  either  day  or  night  scheduling-,  though  more  satisfactory 
for  day  work.  These  methods  fall  into  two  classes :  first,  those  in 
which  the  line  BC  is  constant  for  diameter  and  AD  variable;  and 
second,  those  having  AD  constant  and  BC  variable  for  both  dimen- 
sions. The  former  is  the  more  accurate  and  the  latter  allows  greater 
rapidity  in  scheduling,  but  both  are  very  much  more  rapid  than  any 
direct  measuring  method  and  may  be  read  accurately  to  within  half 
an  ounce  for  small  and  medium  sized  trees,  an  accuracy  as  close  as  is 
needed  in  practical  fumigation.  A  third  form  in  which  AB  was  the 
variable  was  tried,  but  the  difficulty  of  calculation  was  not  readily 
overcome,  so  this  plan  was  discarded  for  the  other  two.* 

We  shall  now  proceed  to  discuss  in  detail  the  two  preferred  forms 
of  apparatus  for  optical  measurement  by  direct  vision. 

THE  "ACCUKATE"  METHOD. 

The  practical  difficulty  that  had  to  be  overcome  in  the  develop- 
ment of  an  optical  method  was  the  establishment  of  what  surveyors 
call  a  base  line,  that  is.  an  accurately  measured  reference  line.  Re- 
ferring again  to  the  diagram  figure  3.  the  adjustment  of  the  instru- 
ment provides  for  the  proper  proportioning  of  the  lines  AB  and  BC. 
Now  if  we  accurately  measure  the  base  line  AD  we  will  have  the  size 
of  DE  with  the  same  accuracy.  In  the  "rapid"  method  described 
below  the  length  of  AB  is  only  approximately  determined  by  the  way 
the  orchard  is  laid  out,  but  for  greater  accuracy  this  distance  must 
be  actually  measured. 

Since  it  is  difficult  to  place  the  end  of  the  tape  in  the  center  of  the 
tree  it  is  entirely  practical  to  measure  not  the  whole  distance  AB,  but 
only  that  from  the  eye  to  the  nearest  point  on  the  tree  giving  AD  — 
^DE,  from  which  it  will  be   quite  as  easy  to  calculate  the  dimensions. 

The  apparatus  consists  of  a  sighting  diagram  and  a  specially  grad- 
uated tape  reading  in  ounces.  A  different  diagram  will  be  required 
for  each  different  basis  of  calculation,  as  will  be  explained  below. 


*  Mr.  0.  E.  McFadden  of  Fullerton,  to  whom  fumigators  are  indebted  for  great 
improvements  in  handling  large  tents  and  who  has  also  been  working  for  some 
time  to  develop  methods  of  optically  measuring  tents,  tells  me  that  he  has  nearly 
perfetced  an  apparatus  working  on  this  principle. 


The  process  of  measuring  a  tree  when  done  by  one  person  consists 
in  attaching  one  end  of  the  tape  to  the  nearest  point  on  a  tree  or  tent, 
then  backing  off  until  the  width  of  the  tree  just  fills  the  diagram. 
If  the  top  of  the  tree  also  corresponds,  the  graduation  on  the  tape 
indicates  the  ounces  that  should  be  used.  A  series  of  marks  on  the 
diagram  indicates  the  amount  to  add  or  subtract  for  high  or  low  trees. 


& 


*^^fc2K£!* 


Pig.  4. — Measuring  the  tree  by  the  use  of  a  tape,  the  ' '  accurate ' '  method. 

If  instead  of  attaching  the  tape  to  the  tree  the  end  is  held  in  place 
by  a  boy  more  rapid  work  will  be  done.     In  this  case  the  scheduler 

will  hold,  in  his  left  hand,  the  scheduling 
board  to  which  the  sighting  diagram  is 
attached  and  allow  the  tape  to  slip  be- 
tween the  fingers  of  the  same  hand. 
With  the  right  hand  he  holds  his  pencil 
and  adjusts  the  tape.  The  procedure  is 
as  follows :  The  scheduler  walks  to- 
wards the  tree  to  be  measured,  slacking 
his  pace  as  the  tree  about  fills  the  dia- 
gram, while  the  boy  continues  until  he 
reaches  the  tree,  thus  pulling  the  tape 
into  the  proper  position.  The  fumigator 
in  the  meantime  has  determined  the 
height  of  the  tree,  and  as  soon  as  his 
helper  announces  having  reached  the  tree 
both  start  to  the  next  position,  the  sched- 
Fig.  5. — Tree  as  seen  through  uler,  having  noted  the  graduation  of  the 
the  diagram.  For  such  a  tree  tape,  pulled  it  back  ready  for  the  adjust- 
the  taPe  ment  for  the  next  tree,  added  or  sub- 
tracted  the  half  ounce  or  more  if  the  tree 


reads  4,  5,  or  6  ounces. 


8 


proved  high  or  low  and  set  down  the  proper  dosage  on  the  schedule 
sheet.  All  this  is  done  in  much  less  time  than  it  takes  to  describe  the 
process.  Two  rows  may  be  taken  at  once,  the  helper  moving  across 
from  side  to  side,  going  first  to  the  larger  and  then  to  the  smaller  of 
each  pair  of  trees.  By  following  this  method  the  scheduler  may 
proceed  down  between  the  rows  scarcely  stopping  as  he  measures  the 
trees. 

The  most  convenient  means  of  holding  the  chart  at  a  constant 


Fig.  6. — Scheduling  diagram  in  which  tape  reading  is  diminished 
for  shorter  trees. 


Fig.  7. — Diagram  in  which  tape  reading  is  raised  or  lowered 
for  high  or  low  trees. 

distance  from  the  eye  is  by  the  use  of  a  light  wire  around  the  hat- 
band. The  end  of  the  wire  is  bent  into  a  hook,  against  which  the  chart 
rests  when  making  an  observation.  The  method  of  determining  the 
point  at  which  to  bend  the  wire  is  described  below. 


THE  " RAPID"  METHOD. 

For  practical  work  the  base  line  can  be  determined  accurately 
enough  by  the  scheduler  locating  himself  by  the  way  the  orchard  is 
laid  out,  and  one  man  can  schedule  four  rows  at  a  time  almost  or  quite 
as  rapidly  as  by  guess. 

The  apparatus  consists  of  an  arrangement  for  holding  a  loop  of 
steel  wire*  at  a  constant  distance  from  the  face  which  can  be  so  bent 
as  to  conform  with  the  shape  of  the  tree,  being  adjustable  both  for 
height  and  width. 

In  order  to  obtain  uniform  readings  with  this  instrument  it  is 


10 


-Positions  to  stand  in  scheduling  an  orchard. 


i  I 


-•.£*% 


"fcfiS 


Fig.  9. — Scheduling  an  orchard  planted  in  diagonal  rows. 


11 


necessary  to  hold  the  chart  at  a  constant  distance  from  the  eye  as  with 
the  ' '  accurate ' '  method,  and  one  must  also  stand  at  a  uniform  distance 
from  the  tree  to  be  measured.  The  best  position  for  this  purpose  is 
the  middle  point  between  the  rows. 

The  immediately  adjacent  trees  are  too  close  to  accurately  measure, 
but  the  next  trees  are  usually  well  in  view  or  will  become  so  by  taking 
a  side  step  in  such  a  direction  that  the  distance  to  the  tree  in  question 
is  not  changed.  In  the  case  of  a  very  large  tree  it  may  be  necessary 
to  approach  till  just  between  two  adjacent  trees,  so  as  to  bring  the 
whole  tree  in  view.  The  distance  AB  must  be  varied  in  adjusting 
the  instrument  according  to  the  position  at  which  one  will  have  to 
stand  in  scheduling  the  orchard. 


Fig.  10. — Appearance  of  tree  through  the  loop. 


THE  CALCULATION. 


After  the  dimensions  of  a  tree  are  obtained  by  any  method  of 
measurement  we  have  still  the  determining  of  the  proper  dose  corre- 
sponding with  the  size.  This  is  too  complicated  a  matter  to  under- 
take in  the  field,  so  that  all  practical  methods  of  measurement  must 
be  combined  with  a  rapid  means  of  accurate  calculation,  and  no 
method  that  does  not  provide  for  variations  in  calculation  will  be 
acceptable. 


*  I  desire  to  acknowledge  the  suggestion  of  the  use  of  a  steel  tape  made  to  me 
by  Mr.  McFadden.  My  apparatus  had  been  based  on  rigid  bars  measuring  height 
and  diameter.  The  tape  which  measures  the  distance  over  instead  of  height  makes 
the  apparatus  somewhat  simpler  in  construction  and  is  fully  as  accurate. 


12 


The  method  of  marking  tents  illustrated  in  Bulletin  No.  152  has 
this  fatal  defect,  because  as  soon  as  measurement  becomes  the  regular 
practice  the  significance  of  variations  which  many  fumigators  regu- 
larly make  in  scheduling  tents  can  be  tested  out  and  their  value  accur- 
ately determined  and  incorporated  in  the  system  of  scheduling.  In 
the  direct  measurement  of  tents  the  calculation  may  be  made  before- 
hand and  presented  in  tabular  form,  in  which  case  a  series  of  tables 


Fig.  11. — Scheduling  trees  by  the  rapid  method. 


must  be  used  to  accord  with  the  different  strength  of  cyanide  desired 
or  the  different  basis  of  calculation.  The  charts  described  below 
afford  a  new  and  improved  means  of  obtaining  the  dose. 

In  the  two  new  methods  of  measurement  here  described  difference 
in  dosage  is  provided  for  in  the  adjustments  of  the  instruments  and 
difference  in  basis  of  calculation-  by  using  different  tapes  or  charts. 
No  one  has  heretofore  pointed  out  the  fact  that  two  entirely  different 
factors  enter  into  the  determination  of  the  amount  of  cyanide  to  use. 
For  instance,  fumigators  were  found  to  vary  all  the  way  from  2  to 
7%  ounces  for  a  10-foot  navel  orange  having  the  two  dimensions 
approximately  equal.  This  we  may  call  a  difference  of  dose,  but  two 
fumigators  having  the  same  dose,  say  5  ounces,  for  a  10-foot  tree  may 
nevertheless  vary  from  7  to  32  ounces  in  their  judgment  of  the  proper 
dose  for  a  20-foot  tree.  Such  differences  represent  different  methods 
of  calculating  the  rate  of  increase  of  dose  to  correspond  with  increase 
of  size.    This  we  will  call  difference  of  basis  of  calculation. 


13 


THE  DOSE. 


The  original  determination  of  the  dose  in  cyanide  fumigation  was 
for  a  12-foot  tree,  as  made  by  Mr.  Morse  of  this  Station  (Bulletin 
No.  71)  for  the  killing  of  the  cottony  cushion  scale,  amounted  to  8 
ounces  of  cyanide.  Mr.  Coquillett  about  the  same  time  (Report  U.  S. 
Dept.  of  Agr.,  1885)  experimented  with  10-foot  trees,  and  his  deter- 
mination was  4.6  ounces  of  cyanide. 

Subsequently  many  tables  have  been  published,  in  most  of  which 
one  can  only  guess  which  items  represent  actual  determinations  of 
killing  strength  and  which  are  determined  mathematically. 

In  Bulletin  No.  152  (page  7)  the  dose  actually  given  by  twenty- 
three  fumi gators  to  the  same  sized  tree  (about  8  feet)  was  tabulated, 
and  showed  a  range  from  1  to  7^/2  ounces,  with  an  average  for  San 
Bernardino,  Los  Angeles,  and  Orange  counties  of  3.2,  3.6,  and  4.8, 
respectively,  the  latter  largely  based  upon  purple  scale,  which  prob- 
ably requires  about  that  ratio  of  increase  over  the  dose  for  black  scale. 
The  latest  determination  is  that  made  by  Woglum  for  purple  scale 
of  HV2  ounces  for  a  tree  10.36  feet  high  by  12.73  in  diameter,  corre- 
sponding about  with  a  11%-foot  tree  of  equal  dimension. 

In  order  to  compare  these  systems  it  will  be  necessary  to  reduce 
them  to  a  uniform  size  of  tent,  and  while  perhaps  not  exactly  fair 
the  best  method  for  such  reduction  is  to  adopt  the  method  calculation 
used  bv  each.    This  gives  for  a  10-foot  tree : 


cottony  cushion  scale 

Morse 

4.5  oz. 

Coquillett 

4.6  oz. 

black  scale 

Average  practice 

4      oz. 

purple  scale 

Average  practice 

6      oz. 

Woglum 's  table 

iy-±  oz. 

The  largest  recommendation  I  find  is  that  of  Pease,  for  red  scale, 
of  8  ounces,  though  the  red  usually  receives  a  dose  intermediate  be- 
tween that  for  the  black  and  the  purple  scale. 

THE  BASIS  OF  CALCULATION. 

When  Morse  published  the  original  table  for  the  dosage  of  trees 
he  assumed  that  the  correct  basis  of  calculation  was  the  cubic  contents 
of  the  tents  and  prepared  his  table  on  that  basis,  giving  1  ounce  of 
cyanide  to  each  145  cubic  feet.  All  of  the  early  writers  about  fumi- 
gation agreed  with  Morse  in  the  method  of  calculation,  only  suggesting 
changes  in  the  strength  of  the  dose.  Practical  fumigators,  however. 
soon  began  to  deviate  from  the  published  tables  b}^  weakening  the 


14 

dose  of  the  larger  trees  and  strengthening  that  of  the  smaller  ones, 
and  that  has  become  now  the  universal  practice  of  California  fumi- 
gators,  though  they  differ  widely  among  themselves  as  to  the  amount 
of  variation  from  a  volume  basis. 

The  first  table  published  recognizing  this  tendency  is  that  of  Craw 
in  1891.  The  first  part  of  his  table  is  obtained  by  multiplying  the 
height  by  the  breadth  and  dividing  by  24,  and  the  latter  part  shows 
a  further  weakening  of  the  dose,  probably  to  approximate  what  he 
found  to  be  actual  practice.  This  table  has  been  the  basis  of  several 
others,  none  mathematically  consistent,  but  apparently  more  nearly 
justified  by  experience  than  any  table  calculated  by  the  Morse  basis 
of  volume. 

The  only  suggestion  hitherto  made  towards  a  method  of  calculation 
corresponding  with  the  experience  of  fumigators  was  in  Bulletin  No. 
152.  This  suggestion  was  a  tentative  recommendation  that  since  the 
tents  now  in  use  leak  gas  very  freely  it  might  be  justifiable  to  dis- 
regard volume  entirely  and  dose  the  trees  in  accordance  with  amount 
of  tent  surface ;  that  is,  in  proportion  to  the  leakage  area,  and  a  table 
was  presented  showing  this  system  as  applied  to  tents  marked  to 
indicate  the  dosage.  Since  the  publication  of  this  suggestion  at  least 
three  writers  have  adopted  it.  One  of  whom,  Mr.  Woglum,  has  ex- 
perimented in  California. 

It  is  very  evident  that  leakage  is  a  prime  factor  in  determining 
the  relative  amounts  of  cyanide  to  use  in  tents  of  different  size,  but 
there  may  be  other  important  factors,  such  as  absorption  of  gas  by 
tht  plant,  and  even  for  leakage  the  area  basis  of  calculation  is  only 
an  approximation  and  not  mathematically  correct,  as  supposed  by 
those  who  have  adopted  it. 

The  Experiment  Station  proposes  to  investigate  at  once  the  factors 
concerned  in  the  basis  of  calculation  and  may  later  be  in  a  position 
to  make  definite  recommendations,  and  in  the  meantime  will  have  to 
be  content  in  presenting  a  statement  of  the  actual  practice  of  fumi- 
gators and  furnish  means  of  calculating  according  to  whatever  basis 
a  fumigator  may  desire  to  adopt. 

No  one  at  the  present  time  follows  strictly  the  Morse  or  volume 
basis  of  calculation.  This  fact  is  perhaps  largely  because  no  one  uses 
the  tight  tents  such  as  were  in  vogue  during  the  early  days  of  fumi- 
gation. According  to  this  system,  a  20-foot  tree  would  require  eight 
times  the  dose  of  a  10-foot  tree.  It  may  be  that  if  tight  tents  are 
again  resorted  to  we  may  return  to  a  volume  basis  of  calculation. 

The  Area  basis  in  which  a  20-foot  tree  receives  four  times  the  dose 


15 


of  a  10-foot  tree  was  suggested  by  this  Station  in  1903,  and  is  that 
advocated  by  Mr.  Woghim.  This  amount  is  exceeded  by  some  of  our 
fumigators  and  may  be  too  low  when  tents  tighter  than  the  average 
are  employed,  but  is  probably  as  safe  a  basis  to  adopt  as  any  until 
our  knowledge  of  the  matter  is  a  little  more  advanced. 


Fig.  12. — Diagram  showing  the  actual  practice  of  thirty  fumigators  in  the 
calculation  of  large  and  small  trees. 

The  Linear  basis  in  which  the  20-foot  tree  receives  twice  as  much 
as  the  10-foot  tree  is  certainly  nearer  the  practice  of  a  majority  of 
our  fumigators  than  any  other  basis  of  calculation,  but  whether  they 
are  justified  in  this  remains  to  be  determined.  I  know  of  no  theo- 
retical reasons  justifying  this  basis  of  calculation,  but  can  not  condemn 
it  with  our  present  inadequate  understanding  of  the  facts  upon  which 
a  correct  calculation  must  depend. 

A  very  few  fumigators  have  adopted  a  uniform  basis  of  dosage, 
but  only  for  orchards  in  which  the  trees  do  not  present  excessive 
variation.  There  is,  of  course,  no  justification  in  this  practice  from 
the  standpoint  of  efficiency  of  the  fumigation,  but  the  practical  con- 
venience of  method  in  the  field  may  compensate  for  the  lack  of  econ- 


16 


omy.     The  dose  must  be  made  large  enough  for  the  largest  trees  and 
is  larger  than  need  be  for  all  others. 

Figure  12  shows  the  actual  practice  of  thirty  fumigators  by  which 
one  can  see  at  a  glance  b}'  the  relative  height  of  the  vertical  lines  how 
the  judgment  of  our  fumigators  stand  as  to  the  proper  basis  of 
calculation. 

METHODS  OF  CALCULATION. 

It  will  be  desirable  to  provide  means  of  calculating  on  a  volume 
an  area  and  a  linear  basis  for  each  of  the  three  methods  of  measuring 
here  described.    The  formulae  for  these  three  bases  of  calculation  are : 


Volume    v  =  -*/  ( h  — 

i> 

Area         a  =  2?r  rh. 

h 
Linear      1  =  r  -f  — . 

The  measurements  actually  made  are : 
Diameter  d  =  2r. 

Circumference    c  =  2t. 

Distance  over    o  =  ~  +  2h  —  zr=  2h  -f-  (*-  —  2)  r. 

and  the  values  of  r  and  h  are : 

Radius     r  =  -~~.      =  tt-. 

2  Z7T 


Height     h  =  \ 


2      V    7T  2    / 


In  calculating  the  tables  for  direct  measurement  the  most  con- 
venient formulae  are : 


1-.V       ]i> 


7T 


9 


1==     --{-2o  — c. 

IT 

which  are  so  calculated  that  when  2o  =  c  the  last  term  becomes  zero. 
This  is  the  shape  of  the  shortest  and  broadest  trees ;  with  higher  trees 
o  being  greater  than  half  of  c  the  last  term  gives  the  corresponding 
increment. 


17 

For  the  optical  methods  an  average  navel  orange  tree  is  a  more 
satisfactory  standard  shape  in  which  2r  =  h  or  h  =  d,  and  h  —  d  = 

o  —  (1  — - —  ,    the  formulae  are : 

a  =  ?rd2  +  7rd  (h—d). 

l  =  d+~(h  —  d). 

in  which,  as  before,  the  last  term  is  zero  with  the  standard  shape  and 
gives  the  increment  when  the  dimensions  vary. 

The  following  constants  will  be  found  useful  for  actual  calcu- 
lations : 

t  =  3.1416,  16^  =  50.2656,^=9.8696,  12*- =118.4352,  -=.3183, 

7T 

~  =  1.5708,  --  =.7854,  -^=6545,  1-^7"  =  2.0708,  —L=. 00844, 
-^=.019894,  J—  =.17724,  f'~V2?  =  4.9109,  |3    1^=1.15186. 

16tt  \    tt  I       qit 

The  method  of  using  these  formulae  and  constants  Avill  be  seen 
from  the  following  example  :  Calculating  on  the  area  basis,  if  c  =  20, 
c2  =  400,  400  X  .31831  ==  127.324  square  feet  when  o  =  Jc  or  10  feet. 
If  o  =  12  feet  then  10  X  (24  — 20)  =40,  127.324  +  40=167.324 
square  feet,  and  every  2  feet  in  value  of  o  adds  40  square  feet  to 
the  surface  of  the  tent. 

GEAPHIC  CALCULATION. 

The  calculation  of  tents  can  be  made  very  rapidly  and  accurately 
by  employing  a  graphic  method  instead  of  figuring  out  each  case  by 
the  use  of  the  above  formulae.  Such  a  diagram  was  illustrated  in 
Bulletin  No.  152  for  volume  calculations,  but  the  method  of  its  con- 
struction was  not  described.  One  of  the  optical  methods  of  measuring 
here  recommended  involves  the  practical  use  of  such  a  diagram,  so  the 
construction  of  these  diagrams  will  be  described  below. 

The  dimensions  chosen  for  the  width  of  this  diagram  were  5% 
inches  and  a  loop  of  steel  wire  was  taken  of  such  length  that  when 
the  ends  were  placed  at  the  distance  apart  of  5%  inches  and  so  held 
as  to  correspond  with  the  normal  shape  of  a  tent  the  height  was  also 
5%  inches. 


18 

The  length  of  this  tape  amounts  to  14%  inches,  as  calculated  from 
the  formula  for  o  previously  given.  Lay  off,  therefore,  14%  inches 
along  the  top  of  the  chart  and  draw  a  diagonal.  Obviously  when 
one  end  of  the  tape  is  fastened  to  the  upper  angle  of  the  chart  and 
the  other  brought  to  any  point  on  this  diagonal  line,  provided  the 
ends  lay  parallel  with  the  upper  edge  of  the  chart,  the  projecting  loop 
will  have  the  height  and  width  equal,  and  the  second  set  of  formulae 
given  above  will  apply.  An  inspection  of  these  formulae  will  show 
that  the  dose  varies  according  to  its  cube  root  in  the  case  of  volume 
basis,  according  to  its  square  root  for  area  and  directly  for  linear 
calculations.  In  the  three  charts  here  presented  the  dose  of  16  ounces 
is  chosen  to  correspond  with  the  maximum  size  of  the  loop  and  the 
doses  1-15  are  laid  off  on  the  diagonal  line  in  the  ratio  of  the  roots  of 
these  numbers.  Each  dose  will  correspond  with  a  curve  which  inter- 
sects the  diagonal  line  at  the  points  just  laid  off.  Other  points  on 
these  curves  can  be  obtained  by  drawing  other  oblique  lines  and  com- 
puting the  relative  position  of  any  particular  dose  and,  then,  with  the 
use  of  two  triangles,  lay  off  the  other  doses  in  the  same  proportion  as 
they  occur  on  the  diagonal  line.  Two  or  three  oblique  lines  on  either 
side  of  the  diagonal  will  enable  one  to  locate  all  the  curves  in  a  very 
satisfactory  manner. 

USE  OF  CHART  FOR  CALCULATING  DIRECT  MEASUREMENTS. 

One  may  use  this  diagram  for  calculating  the  dosage  from  direct 
measurements.  If  the  measurements  are  taken  in  terms  of  h  and  d, 
one  lays  off  along  the  diagonal  line  equal  spaces  corresponding  to  the 
dimensions ;  now  lay  a  card  on  the  chart,  keeping  it  square  with  the 
edges  of  the  chart,  and  make  it  cross  the  diagonal  line  at  the  two 
dimensions  and  the  corner  of  the  card  will  indicate  the  dose.  If  the 
height  is  the  larger,  read  above  the  diagonal;  if  smaller,  read  below. 
(See  fig.  13.) 

When  the  dimensions  are  in  terms  of  c  and  o,  draw  another  oblique 
line  along  the  upper  ends  of  the  curves  and  graduate  it  as  before, 
determining  the  dose  by  the  use  of  a  card  in  the  same  manner  from 
the  graduations  of  this  line. 

The  accurate  graduation  of  the  oblique  lines  is  not  a  difficult 
operation.     The  methods  are  as  follows : 

FOR  HEIGHTS  AND  BREADTH. 
Graduate  the  diagonal  line,  for  measurements  in  terms  of  h  and  d : 


19 


First,  lay  a  ruler  along  the  top  of  the  chart  as  shown  in  fig.  13, 
bringing  14%  inches  at  the  upper  right-hand  corner  of  the  chart. 

Second,  connect  the  10-inch  division  with  the  dose  desired  as  indi- 
cated along  the  diagonal  line,  say  6  ounces,  as  shown  in  the  figure. 

Third,  draw  parallel  lines  from  the  ruler  to  the  diagonal  line  from 
each  inch  division.  In  this  way  graduate  the  whole  length  of  the 
diagonal  line.  Each  division  so  marked  will  correspond  with  a  foot 
in  height  or  width  of  tree. 


Fig.  13. — Method  of  graduating  the  diagonal  line  for  a  6-ounce  dose  for  a  10-foot 
tree,  and  the  use  of  a  card  showing  that  on  this  dose  and  basis  a  tent  12  feet 
high  and  10  feet  across  corresponds  with  7%  ounces. 


FOR  DISTANCE  OVER  AND  AROUND  TENT. 

Graduate  an  oblique  line  to  be  drawn  along  the  upper  ends  of  the 
curves  for  values  in  c  and  o : 

First,  place  a  card  on  the  chart  with  the  corner  at  the  dose  desired 
for  the  10-foot  tree  (fig.  14,  showing  4  ounces),  keeping  the  cord  square 
with  the  edges  of  the  chart  and  marking  the  points  of  intersection 
with  the  oblique  line.  The  dimensions  of  a  standard  shaped  tent  are 
20.7  feet  and  31.4  feet,  respectively;  therefore,  mark  these  points  on 
the  oblique  line  and  also  mark  on  the  card  the  points  where  the  oblique 
line  touches  the  edge  of  the  card. 

Second,  draw  a  line  from  one  of  the  points  marked  on  the  card  and 
mark  along  it  ten  equal  distances  and  make  a  division  at  the  end 
seven-tenths  as  long  as  the  others.  Now  draw  a  line  from  the  end  of 
this  short  division  to  the  other  mark  on  the  card  and  a  series  of  parallel 


20 


lines  through  the  graduations,  as  shown  in  figure  15.  These  parallel 
lines  intersect  a  line  connecting  the  two  marks  first  made  on  the  card, 
each  giving  the  correct  distance  to  correspond  with  a  foot  on  the 
oblique  line. 

Third,  the  short  division  will  locate  the  20-foot  point  and  then  the 
whole  line  may  be  graduated  in  feet.  It  will  thus  take  but  a  few 
minutes  to  graduate  a  chart  to  correspond  to  any  dosage  desired  and 
the  dose  can  be  determined  from  any  given  dimensions  with  great 
facility  and  accuracy,  according  to  any  desired  system  of  scheduling, 
and  avoid  entirely  any  recourse  to  mathematical  calculation. 


1 

rUMIGATOR'S  SCHEDULING  CHABT. 

,        c 

cultural  Experiment  Station  — University  of  California.                                    VOLU.Y1  E 

B 

r 

i_ 

' 

~v~*\_\   \\\\\\\\ 

4 

r 

^ 

j 

A 

^~ 

=£pi 

?i--" 

[ 

^ 

i 

-' : 

-" 

'*i^3f\' 

"~"  _.-- 

I 

^uU^nT^ 

(.. Location  of  Plot 

Fig.  14. — Method  of  graduating  the  line  used  in  calculating 
from  tent  measurements. 


USE  OF  CHABT  FOR  GRADUATING  TAPES. 

The  graduation  of  the  tapes,  for  the  "accurate"  optical  method 
of  measurement  may  be  done  either  by  mathematical  calculation  or 
by  the  use  of  the  charts.  The  exact  length  of  the  tape  is  only  a  matter 
of  convenience,  since  the  adjustment  of  the  distance  the  apparatus 
is  held  from  the  eye  can  be  varied  through  rather  a  wide  range.  It 
is  only  necessary  that  the  graduations  be  correctly  placed  as  regards 
each  other.  As  has  already  been  shown,  these  relationships  are  the 
roots  of  the  numbers,  just  the  quantities  that  have  been  used  in  con- 
structing the  charts. 

To  graduate  the  tapes  mathematically  one  would  multiply  succes- 
sively the  roots  of  1,  2,  3,  etc.,  by  such  a  constant  that  the  highest 
number  would  give  a  convenient  length  of  tape  and  lay  off  each  of  the 
products  on  the  tape. 


Scheduled                     191 by FUMIGATOR'S  SCHEDULING  CHART.                                                   des,gNED  by  c.  w.  woodworth. 

Dose  for  10  foot  tree               ounces.    Agricultural  Experiment  Station  — University  of  California.                                             AREA    BASIS. 

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DESIGNED    BY   C.    W.    WOODWORTH. 

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Instead  of  performing  all  these  multiplications  the  same  end  may 
be  secured  by  graduating  the  diagonal  line  in  the  manner  previously 
described,  but  making  the  number  of  divisions  such  that  they  will 
conform  to  feet  in  the  length  of  the  tape  and  give  a  convenient  length. 
Thus,  perhaps,  a  32-foot  tape  may  be  a  convenient  length  and  the 
diagonal  line  would  then  be  divided  into  half  inches.  Calling  every 
half  inch  a  foot,  the  tape  could  be  graduated  according  to  the  inter- 
sections of  the  curves  and  the  diagonal  line. 

PKECAUTIONS  AND  ADJUSTMENTS. 

No  system  of  measurement  or  calculation  can  be  devised  that  will 
not  be  more  or  less  inaccurate  in  the  hands  of  an  ignorant  or  careless 
operator,  and  even  in  the  hands  of  the  most  intelligent  and  careful 
scheduler  there  will  be  a  certain  range  of  error. 

It  is  a  wise  plan  to  try  to  determine  not  only  the  sources  of  error, 
but  also  the  amount  of  error  each  is  liable  to  introduce  into  the  final 
result.  With  this  in  view  let  us  compare  the  three  more  important 
methods  of  measurements. 

Errors  with  marked  tents.— When  tents  are  thrown  over  a  tree  the 
center  rarely  falls  twice  in  the  same  relative  position.  A  single  row 
of  marks  down  each  side  may  sometimes  give  a  reading  several  ounces 
smaller  than  though  the  line  went  over  the  highest  point.  This  defect 
has  been  partly  overcome  in  the  marking  covered  by  Mr.  Morrill's 
patent,  and  recommended  by  Mr.  Woglum,  by  using  three  lines  with 
the  thought  that  one  of  them  would  be  likely  to  lay  over  the  treetop. 
My  own  markings  attempted  to  gain  the  same  end  by  making  the  lines 
long.  Possibly  the  best  plan  is  that  first  suggested  by  Mr.  Payne, 
referred  to  in  Bulletin  No.  152,  of  making  the  marks  take  the  form 
of  rings,  in  which  case  the  sum  of  the  largest  and  smallest  distance 
would  be  over  the  highest  point.  This  plan  of  marking  is,  however, 
also  covered  by  a  patent.  Even  here  the  dimensions  may  not  be 
entirely  correct  if  the  tree  is  irregular  in  shape.  With  a  detached 
measuring  device  one  could  be  quite  sure  of  getting  his  error  on  the 
safe  side,  and  with  any  form  of  marked  tents  there  is  still  room  to 
exercise  judgment,  even  to  the  extent  at  times  of  calling  a  dimension 
different  from  anything  shown  by  the  marks. 

The  circumference  taken  by  stepping  is  another  source  of  error 
of  considerable  magnitude,  as  shown  by  the  fact  that  only  a  few  people 
are  successful  in  stepping  in  a  way  to  correspond  with  tape  measure- 
ments. The  plan  of  pacing  around  the  tent  was  first  suggested  by 
myself,  but  there  is  no  saving  of  time  as  compared  with  the  use  of 


22 

the  tape.    With  the  tape  the  circumference  becomes  the  most  accurate 
of  any  measurements  it  is  possible  to  make  of  fumigation  tents. 

A  third  source  of  error  of  no  small  extent  is  the  use  of  incorrectly 
calculated  tables.  One  such  table  has  been  extensively  used  in  which 
errors  occur  amounting  to  25  per  cent.,  both  above  and  below  the 
correct  dose.  It  should  be  noted  that  Morrill's  patent  covers  the  style 
of  table  recommended  by  Mr.  Woglum. 

ADJUSTMENTS  AND  ERRORS  IN  THE  ' '  ACCURATE ' '  METHOD. 

Both  optical  methods  require  a  preliminary  adjustment  of  the 
wire  about  the  hatband  so  as  to  hold  the  diagram  a  constant  distance 
from  the  eye.  This  is  not  difficult  to  do,  and  the  amount  of  the  error 
introduced  by  faulty  adjustment  can  be  seen  in  terms  of  the  dose. 

The  adjustment  is  quickly  made  by  having  some  one  hold  a  10-foot 
pole  in  one  hand  and  the  end  of  the  tape  in  the  other,  so  that  the  end 
of  the  tape  is  5  feet  from  the  pole.  Now  taking  such  a  position  that 
the  number  of  ounces  corresponding  with  the  10-foot  tree  is  indicated 
on  the  tape  at  the  distance  of  the  eye  when  the  tape  is  held  straight, 
move  the  diagram  until  the  length  of  the  pole  corresponds  with  the 
width  of  the  diagram,  then  bend  the  wire  to  maintain  this  width. 

The  chief  chances  of  error  are  (1)  a  shifting  of  the  position  of  the 
hat  making  the  distance  of  the  eye  to  the  diagram  different;  (2)  fail- 
ure to  properly  judge  the  location  of  the  edge  of  the  tree;  (3)  irreg- 
ular trees.  The  first  should  be  entirely  avoided,  the  second  is  not 
very  liable  to  make  a  large  error,  and  the  third  can  be  avoided  by 
making  several  readings  and  averaging  the  results  when  the  tree  is  not 
of  the  usual  shape. 

The  facility  of  re-scheduling  trees  is  a  particularly  valuable  feature 
of  both  optical  methods,  because  the  scheduler  can  check  himself  up 
or  be  checked  up  by  others.  Where  tents  have  to  be  placed  on  a  tree 
before  it  can  be  measured  a  scheduler  can  be  morally  certain  that  his 
mistakes  will  not  be  found  out. 

Added  to  these  sources  of  error  is  the  question  of  the  effect  of  the 
weight  of  the  tent  in  reducing  the  size  of  a  tree.  Errors  are  most 
likely  to  be  made  on  the  safe  side.  The  only  way  for  a  scheduler  to 
develop  his  judgment  in  this  matter  is  by  doing  more  or  less  night 
scheduling  and  comparing  it  tree  by  tree  with  day  scheduling. 


23 


ADJUSTMENTS  AND  PRECAUTIONS  IN  THE  " RAPID"  METHOD. 

To  adjust  the  apparatus,  set  the  end  of  the  pointer  on  the  dose  that 
should  be  given  to  a  10-foot  tree  on  the  diagonal  line.  Place  a  10-foot 
pole  at  the  distance  one  will  stand  in  scheduling  the  trees  in  the  orch- 
ard, then  moving  the  apparatus  toward  or  away  from  the  face  as  may 
be  necessary  in  order  to  make  the  width  of  the  loop  correspond  with 
the  length  of  the  10-foot  pole ;  then  bend  the  end  of  the  wire  to  support 
the  loop  precisely  that  distance  from  the  eye. 

The  most  important  source  of  error  is  the  location  of  oneself  the 
proper  distance  from  the  tree  to  be  scheduled.  By  looking  between 
the  rows  in  both  directions  one  can  come  close  enough  for  practical 
purposes  and  can  determine  quite  readily  the  limit  of  error  by  moving 
the  head  forward  and  backward  till  clearly  beyond  the  correct  location 
and  seeing  the  difference  in  dose  indicated. 

Added  to  this  are  most  of  the  sources  of  error  enumerated  when 
discussing  the  "accurate"  method.  The  only  advantage  the  accurate 
method  has  over  the  "rapid"  method  is  the  accurate  determination 
of  the  distance  from  the  eye  to  the  tree. 


CONCLUDING  REMARKS. 

While  the  questions  involved  in  scheduling  trees  are  thus  seen  to 
be  very  intricate  and  complex,  the  actual  practice  of  scheduling  of 
trees  in  the  field  is  a  comparatively  simple  matter  with  our  new 
methods  and  apparatus — simple  enough,  indeed,  to  be  understood  and 
performed  by  a  child. 

A  brief  but  comprehensive  presentation  of  the  practical  suggestions 
of  the  preceding  pages  will  be  found  in  the  directions  printed  on  the 
reverse  of  Chart  I  and  upon  all  the  charts  as  they  are  now  issued  by 
The  Braun  Corporation,  361-371  New  High  street,  Los  Angeles.  This 
company  has  undertaken  to  supply  the  apparatus  herein  described  at 
a  nominal  price. 


24 


RESUME. 

Scheduling  by  measure  instead  of  guess  is  essential  to  progress  in  fumigation. 

Older  methods  of  measuring  are  not  practical. 

The  method  of  marked  tents  devised  by  this  Station  is  the  most  practical 
means  heretofore  suggested. 

Optical  methods  of  measuring  are  practical  and  much  more  rapid. 

Numerous  forms  of  optical  measurement  have  been  tested,  but  direct  vision 
methods  seem  most  satisfactory. 

Two  methods  are  recommended,  one  more  accurate  for  experimental  work 
and  the  other  very  rapid  for  practical  fumigation. 

The  "Accurate"  method  depends  on  the  use  of  a  tape  to  measure  the 
distance  from  the  tree  to  the  scheduler. 

The  "Rapid"  method  employs  a  loop  of  steel  wire,  the  end  of  which  points 
to  the  dose  on  a  chart  as  soon  as  the  loop  is  made  to  correspond  with  the  size 
of  the  tree. 

The  calculation  of  the  dose  is  a  very  complicated  matter,  and  practice  differs 
widely  both  as  to  the  amount  to  use  for  a  given  size  of  tree  and  also  the  rate 
of  change  for  increase  in  size. 

A  ten-foot  navel  orange  is  suggested  as  a  standard  for  stating  the  dose  and 
the  original  recommendations  and  actual  practice  is  given. 

The  basis  of  calculation  is  at  present  hopelessly  involved.  The  practice  of 
fumigators  is  shown  and  the  area  basis  tentatively  suggested. 

The  formulae  for  calculating  according  to  the  different  bases  are  presented 
in  a  new  and  very  convenient  form. 

A  graphic  method  of  obtaining  dosage  is  presented  as  a  substitute  for  mathe- 
matics, greatly  simplifying  the  process  of  calculation. 

The  charts  presented  furnish  the  most  rapid  and  most  adaptable  method  of 
obtaining  dosage  from  direct  measurements. 

They  are  also  the  most  convenient  means  of  graduating  tapes  for  the 
"accurate"  optical  method  of  measuring. 

The  sources  of  error  in  direct  measuring  are  the  shifting  of  the  tent,  the 
irregularity  of  the  tree,  pacing,  and  inaccurate  dosage  tables. 

Accuracy  by  the  optical  method  requires  careful  adjustment,  that  the  ad- 
justment be  not  disturbed,  and  that  irregular  trees  be  re-scheduled. 

Re-scheduling  affords  the  best  possible  means  of  improving  the  judgment  in 
scheduling. 

Scheduling  by  the  new  methods  is  very  easily  understood  and  performed  as 
well  as  being  rapid  and  accurate. 


